Combinatorial Optimization on Gate Model Quantum Computers: A Survey

TL;DR

This survey reviews various quantum computing approaches for solving combinatorial optimization problems, especially QUBO problems, highlighting recent methods and their potential for industrial applications.

Contribution

It provides a comprehensive overview of quantum algorithms for QUBO problems on gate model quantum computers, including digitized adiabatic, global optimization, and sampling techniques.

Findings

Multiple quantum algorithms are suitable for QUBO problems.

Quantum approaches show promise for industrial optimization tasks.

Different algorithms have varying strengths depending on problem structure.

Abstract

The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of these new devices. These problems are recurrent in industrial applications and they are in general difficult for classical computing hardware. In this work, we provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. We focus mainly on four different approaches including digitizing the adiabatic quantum computing, global quantum optimization algorithms, the quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. We also discuss the quantum algorithms that are custom designed to solve certain types of QUBO problems.